A parsimonious Begriffsschrift [concept notation] for animals James R Hurford.
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Transcript of A parsimonious Begriffsschrift [concept notation] for animals James R Hurford.
A parsimonious Begriffsschrift
[concept notation] for animals
James R Hurford
PHILOSOPHY
speculative, armchair
Deep and careful
reasoning
NEUROSCIENCE
empirical, laboratory
Rigorous controlled
experiments
x (W(x) y (M(y) →L(x,y)))
A) V E
Pragmatics+Semantics
Morphosyntax
Phonology
Phonetics
SOUNDS
MEANINGS
Phonetic transcription: [bru:thus khaizarem nekhawit]
Logical form (e.g. FOPL): Stab(e) & Agent(e,brutus) & Patient(e,caesar)
Phonetics
Acoustic form Motor commands
Semantics
Universe of discourse Mental representations
STARSEARTHHOMEPERSONTOENAIL
Crack open a brain, and what do you find?
No symbols!
The nature of mental representations
Symbolic notations are useful.
“The grasp schema.
1. The role parameters: agent, object, object location, and the action itself.
2. The phase parameters: initial condition, starting phase, central phase, purpose condition, ending phase, final state.” (Gallese & Lakoff, 2005)
“… we have written down symbols (e.g. final state) as our notation for functional clusters. This does not mean that we take functional clusters themselves to be symbolic. The symbols are only our names for functional clusters, which function as neurally realised units” (Gallese & Lakoff, 2005)
A phonetic analogy
SymbolsNon-symbolic
represent-ations
Frege devised a Begriffschrift, a symbolic notation for writing concepts.
This has become First Order Predicate Logic (FOPL).
It is useful to linguists and logicians for representing the meanings of sentences.
Frege, and many modern logicians, posit abstract, non-neural status for their symbols.
The (new) research programme is to develop a symbolic notation for the meanings of sentences with a natural neural interpretation.
The proposed notation builds on
Event-based semantics (Davidson,1967; Parsons, 1990)
Discourse Representation Theory (Kamp & Reyle, 1993)
Conjunctivism (Batali, 2002; Pietroski, 2005)
How this relates to language evolution
Higher animals have no language, but they have private conceptual representations of the world, implemented in functional neural clusters.
Apes and humans share many aspects of the neural representation of scenes.
These are the primitive basis of later evolved public language.
Linguistic/logical formulae are cluttered with entities of too many different kinds.
• Predicates - 1-place, 2-place, 3-place, …
Individual constants
Individual variables
Quantifiers
Role Markers
Connectives
RED, MAN, HIT, GIVE
John, London
x, y, z
,
Agent, Patient, …
&, V, ~
Occam’s razor – a parsimonious entity set for linguistic/logical formulae
• Predicates - 1-place
Individual variables, up to 4
Quantifier (implicit)
Connective (implicit)
RED, MAN, (HIT, GIVE),
JOHN, LONDON
AGENT, PATIENT, …
w, x, y, z
&
Reminder: the representations I propose face two ways: they are convenient symbolic notations (names) …
1.… for linguists and logicians to map onto (a subset of) human language sentences.
2. … to express the neural patterns constituting pre-linguistic thoughts (e.g. in animals and babies).
Therefore, they must meet both linguistic and neural criteria of adequacy.
An unproblematic example
( x y)
DOG(x) & BROWN(x) & CAT(y) & WHITE(y)
Ci sono un cane marrone ed un gatto bianco
Three notational moves:
• Individual constants (proper names) as predicates
• Role markers (Agent, Patient, …) as predicates
• Reducing all predicates to 1-place
Three philosophical themes:
• Abandoning the God’s-eye-view of logic
• Objects in cognition as bundles of features
• Events, scenes, situations are complex objects
Three neuropsychological phenomena:
• Dorsal-ventral separation
• Global and local attention (– simultanagnosia, etc)
• Frame of reference systems
Proper names are proto-logically predicates: the principled unknowability of uniqueness.
FIDO(x) & FELIX(y)
Reminder: Predicate symbols, e.g. CAT, FIDO, “are only our names for functional clusters, which function as neurally realised units.” (Gallese & Lakoff, 2005)
PredictionThere is no agnosia or anomia that affects all and only non-proper names, i.e. affects predicates but not individual constants.
PREDICATESIndividual constants
Animal predicates
Vegetable predicates
Fruit predicates Tool
predicates
Personal name
predicates
x y
Jones(x)
Ulysses(y)
x owns y
Kamp & Reyle, 1993, p.64
Precedent in Discourse Representation Theory
Participant roles (aka theta roles) e.g. Agent, Patient, etc. are predicates.
They just happen to be predicates typically expressed by grammatical relations, e.g. Subject, Direct Object, Indirect Object, rather than by words.
But many roles are signalled by particular words, e.g.
Agent -- by, do, leader Patient -- victim
Beneficiary -- to, get Instrument -- with, use
Locative -- in, at, on
Event semantics (e.g. Parsons, 1990) treats Agent, Patient, etc. as predicates and event verbs as 1-place.
e STAB(e) & AGENT(brutus,e) & PATIENT(caesar,e)
With proper names as predicates:
e STAB(e) & AGENT(x, e) & PATIENT(y, e)
& BRUTUS(x) & CAESAR(y)
The original 2-place predicate STAB is now 1-place, and AGENT and PATIENT have become 2-place.
Valency (arity) is debatable.
Reducing all predicates to 1-place
Motivation: Hurford (2003) claims a correspondence
• between indices for external objects of focal attention, delivered by the dorsal stream, and individual variables w, x, y, z; and
• between categorical judgements about objects’ properties, delivered by the ventral stream, and predicates, such as RED, CAT, MARY.
The brain integrates what these two streams deliver into a single PREDICATE(x) representation.
The 1-place claim is not so radical as it may seem.
In event semantics, the roles (Agent, Patient, etc.) are only 2-place to link them to the event predicate.
e STAB(e) & AGENT(x, e) & PATIENT(y, e)
& BRUTUS(x) & CAESAR(y)
A box notation can likewise relativize the role predicates to the event predicate.
STABAGENT
BRUTUS
CAESAR
PATIENT
e STAB(e) & AGENT(x, e) & PATIENT(y, e)
& BRUTUS(x) & CAESAR(y)
In the box notation:
• Each box is the equivalent of a separate individual variable, x, y, z, …
• The predicates inside a box are equivalent to conjunctions of predicates applying to the variables.
• Items within boxes are unordered.
STABAGENT
BRUTUS
CAESAR
PATIENT
Role predicates are assigned relative to their event contexts.
Dowty’s Proto-Agent and Proto-Patient. A participant can have more or fewer of the prototypical properties of an Agent, e.g. animacy, movement, volition, causation.
What is an Agent for one event (e.g. running) could be a Patient for another event (e.g. chasing).
Predicates are more or less context-relative:
gradable predicates, e.g. BIG
common nouny predicates, e.g. HERO,TABLE
proper nouny predicates, e.g. JOHN, LONDON
Frame of Reference
Judgements are made relative to their contexts.
E.g. Input judged as WHITE in half-light is judged as GREY in full light.
Jokisch & Troje (2003) Fast-striding animals are seen as relatively small, and slow-striding animals are judged to be relatively big.
Sarris (1998) Chickens can be trained to make perceptual judgements such as ‘big for a red cube’ and ‘small for a green cube’.
Jones
Ulysses
owns
x y
Kamp & Reyle, 1993, p.64
(x)
(y)
person book
yx
In any (non-symmetric) 2-place predication, one argument is always distinguished from the other by some property (1-place). That’s how we can tell which role each argument plays.
In symmetric 2-place predications, both arguments have the same role properties.
MEET (john, mary) = MEET (mary, john)
In the traditional notation, argument ordering is superfluous.
JOHN MARY
MEET
Global and local attention
“Forest before trees” – “global structuring of a visual scene precedes analysis of local features” (Navon, 1977:353)
“An initial rapid pass through the visual hierarchy provides the global framework and gist of the scene and primes competing identities through the features that are detected. Attention is then focused back to early areas to allow a serial check of the initial rough bindings and to form the representations of objects and events that are consciously experienced.” (Treisman, 2004:541)
• Global attention searches for individual features in a scene in parallel. Individual features (e.g. RED) pop out.
• Local attention fixes serially on separate objects, up to about 4, binding their conjunctions of features, (e.g. BLUE RED
SQUARE , UP
ARROW )
• These two separate process integrate seamlessly in normal vision (and hearing) to provide a single unified representation of a scene.
Disorders involving global or local attention• Simultanagnosia: patients “can only see one object at a time”, and “cannot make sense of pictures of familiar scenes”.
• Williams Syndrome: impaired global attention
• Down Syndrome: impaired local attention
• Left neglect: failure of orienting response to left visual field
+
Global and local attention
REDYELLOW
PURPLE
SKIRT
DANCE
GIRLGIRL
Quick global attention delivers something like
with predicates only approximately bound
Global and local attention
Another example
KISS
BOY
GIRL
SMILE
Quick global attention delivers
An iconic notation, taking a cue from event semantics
KISS
AGENT BOY
PATIENT GIRL
SMILE
KISS(e) & AGENT(x) &
BOY(x) & PATIENT(y) & GIRL(y) &
SMILE(y)
Boxes correspond to individual variables, e, w, x, y, z.
An iconic notation, taking a cue from event semantics
AGENT GIRL
SMILE
AGENT(y) & GIRL(y) & SMILE(y)
(No ontological distinction between a one-participant event/state and an individual object.)
In relation to the box notation:
• Whole event/scene/situation predicates are those delivered by global attention, unbound to any particular object in the scene. Such a predicate goes in the outer box.
• Such whole-scene predicates can select for scenes with particular numbers of participants.
CHURCHILL
ROOSEVELT
STALIN
THREE
CHURCHILL LEFT
ROOSEVELT MIDDLE
STALIN RIGHT
BETWEEN
A “betweenness situation” necessarily involves three participants.
FACE
PARTEYE
BLUE
PARTEYE
BLUE
PART NOSE
CROOKED
A face with two blue eyes and a crooked nose.
These are private scene representations; aspects of meaning involving public communication are not represented. E.g.
• Active/passive pairs:– Kanzi gave Matata a banana– Matata was given a banana by Kanzi– A banana was given to Matata by Kanzi
• Various Topicalization devices:– Kanzi bit Matata– Matata, Kanzi bit her– It was Matata that Kanzi bit
• Some relative clause or modifying structures:– Kanzi bit the chimp that was screaming– Kanzi bit the screaming chimp– The chimp that Kanzi bit was screaming– The screaming one that Kanzi bit was a chimp
THE ENDThanks for listening.